Finite Group Databasebeta

← #14754542

Subgroups — #14754542

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623035C211yesmaximal, characteristic
2C2×#10622494C211yesmaximal, characteristic, complemented
3C2×#10622493C211yesmaximal, characteristic, complemented
4C2×#10622340C211yesmaximal, characteristic
5#13071205C211yesmaximal, characteristic
6#13068818C211yesmaximal, characteristic, complemented
7#13068817C211yesmaximal, characteristic, complemented
8#13068813C211yesmaximal, characteristic, complemented
9#13068812C211yesmaximal, characteristic, complemented
10#13068810C211yesmaximal, characteristic, complemented
11#13068809C211yesmaximal, characteristic, complemented
12#13068802C211yesmaximal, characteristic, complemented
13#13068334C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#1852C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×C4×C22⋊D11—21no—
19C2×C4×C22⋊D11—21no—
20C2×#66979C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23#10623035—24no—
24#10623035—24no—
25C2×#66946—21no—
26C2×#66945C2211yescharacteristic
27C2×#66945C2211yescharacteristic
28C2×#66945C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×C4⋊C4×D11C2211yescharacteristic
32C2×#66940—21no—
33C2×C11×#107C2211yescharacteristic
34C2×C11×#107C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#380C2211yescharacteristic
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×#66882C2211yescharacteristic
42C2×#66881C2211yescharacteristic
43#10622600C2211yescharacteristic
44#10622600C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622570—21no—
50#10622569—21no—
51#10622494—24no—
52#10622493—24no—
53#10622340C418yescomplemented
54#10622278—21no—
55#10622259—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11D411yescharacteristic
67C22×C22⋊D11D411yescharacteristic
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—22no—
71C2×#4339—22no—
72C2×#4339C2×C414yes—
73C2×#4339Q814yes—
74C22×D44D411yescharacteristic
75C22×C4×D11—21no—
76C22×C4×D11—21no—
77C22×C4×D11—21no—
78C22×C4×D11C2311yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×Dic22D411yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C4×C22⋊D11—28no—
94C4×C22⋊D11—28no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100#66979—22no—
101#66979—22no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C2×#4313—22no—
116C2×#4313—22no—
117C2×#4313C2×C414yescomplemented
118C2×C8×D11—22no—
119C2×C8×D11—22no—
120C2×C8×D11C2×C414yescomplemented
121#66946—28no—
122#66945—22no—
123#66945—22no—
124#66945—22no—
125#66945—22no—
126#66945—22no—
127#66945D414yes—
128C4⋊C4×D11—22no—
129C4⋊C4×D11—22no—
130C4⋊C4×D11—22no—
131C4⋊C4×D11—22no—
132C4⋊C4×D11—22no—
133C4⋊C4×D11D414yes—
134#66940—28no—
135C11×#107—22no—
136C11×#107—22no—
137C11×C22⋊C8C2×C414yescomplemented
138C11×#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C22⋊(C11⋊C8)C2×C414yescomplemented
143(C2×D11)⋊C8C2×C414yescomplemented
144(C2×D11)⋊C8C2×C414yescomplemented
145#66882—22no—
146#66881—22no—
147#66872—22no—
148#66872—22no—
149#66872—22no—
150#66871—22no—
151#20849—111nomaximal, Sylow
152C24×C11C2×D411yescharacteristic
153C23×D11C2×D411yescharacteristic
154C23×D11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—81no—
165C22×C4×C11—81no—
166C22×C4×C11C22×C412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×Q812yes—
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—22no—
171C2×C22⋊D11—22no—
172C2×C22⋊D11—22no—
173C2×C22⋊D11—22no—
174C2×C22⋊D11C4⋊C414yes—
175C2×C22⋊D11C4⋊C414yes—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182#4339—28no—
183#4339—28no—
184#4339—28no—
185#4339—28no—
186C2×D44—22no—
187C2×D44—22no—
188C2×D44C4⋊C414yes—
189C2×C4×D11—24no—
190C2×C4×D11—24no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11—42no—
196C2×C4×D11—81no—
197C2×C4×D11—81no—
198C2×C4×D11—81no—
199C2×C4×D11—81no—
200C2×C4×D11—81no—
201C2×C4×D11—81no—
202C2×C4×D11C22×C412yes—
203C2×C4×D11C22×C412yes—
204C2×C4×D11C2×D412yes—
205C2×C4×D11C2×D412yes—
206C2×C4×D11C2×Q812yes—
207C2×C4×D11C2×Q812yes—
208C2×C4×D11#4112yes—
209C2×C4×D11#4112yes—
210C2×Dic22—22no—
211C2×Dic22—22no—
212C2×Dic22C4⋊C414yes—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11C22×C412yes—
218C2×C8×C11C22×C412yes—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4C2×D412yes—
227C11×C4⋊C4C2×D412yes—
228C11×C22⋊C4—81no—
229C22⋊Dic11—24no—
230C22⋊Dic11—81no—
231(C2×D11)⋊C4—24no—
232(C2×D11)⋊C4—24no—
233(C2×D11)⋊C4—42no—
234(C2×D11)⋊C4—81no—
235(C2×D11)⋊C4—81no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11C2×D412yes—
243C4⋊Dic11C2×D412yes—
244Dic11⋊C4—24no—
245Dic11⋊C4—24no—
246Dic11⋊C4—42no—
247C4×Dic11—24no—
248C4×Dic11—24no—
249C4×Dic11—24no—
250C4×Dic11—42no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8C22×C412yes—
256C2×C11⋊C8C22×C412yes—
257#4313—28no—
258C8×D11—28no—
259C2×#520—111no—
260C2×#428—111no—
261C2×#427—111no—
262C2×#408—111no—
263#2311—111no—
264#1854—111no—
265#1854—111no—
266#1854—111no—
267#1854—111no—
268#1853—111no—
269#1853—111no—
270#1852—111no—
271#1852D1111yescharacteristic, complemented
272#1736—111no—
273C2×#340—111no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11C2×C4⋊C412yes—
281C23×C11C22×D411yescharacteristic
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11C2×C4⋊C412yes—
293C22×D11C2×C4⋊C412yes—
294C22×D11#12012yes—
295C22×D11#12312yes—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—84no—
315C2×C4×C11C2×C4⋊C412yes—
316C2×C4×C11C23×C411yescharacteristic
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×Q811yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C22⋊D11—28no—
323C22⋊D11—28no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11C2×C4⋊C412yes—
339C2×Dic11C2×C4⋊C412yes—
340C2×Dic11#12012yes—
341C2×Dic11#12312yes—
342D44—28no—
343C4×D11—22no—
344C4×D11—22no—
345C4×D11—22no—
346C4×D11—22no—
347C4×D11—84no—
348C4×D11—84no—
349C4×D11—84no—
350C4×D11C4×D414yes—
351C4×D11C4×D414yes—
352C4×D11C22⋊Q814yes—
353C4×D11C22⋊Q814yes—
354Dic22—28no—
355C8×C11—22no—
356C8×C11—22no—
357C11⋊C8—22no—
358C11⋊C8—22no—
359C22×#41—111no—
360C22×M16—111no—
361C23×C8—111no—
362#520—224no—
363#520—224no—
364C2×C4×Q8—221no—
365C2×C4×D4—221no—
366C2×C4×D4—221no—
367C2×C4×D4—221no—
368C2×#117—111no—
369C2×#117—111no—
370C2×#117—111no—
371C2×#117—111no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374C22×C4⋊C4—111no—
375C22×C4⋊C4C2×D1111yescharacteristic
376#428—224no—
377#427—224no—
378C2×#107—111no—
379C2×#107—111no—
380C2×#107C2×D1111yescharacteristic
381C2×#107C2×D1111yescharacteristic
382C2×#106—111no—
383C2×#106—111no—
384C2×#106—111no—
385C2×#106—111no—
386#408—118no—
387C2×C22⋊C8—111no—
388C2×C22⋊C8—111no—
389C2×C22⋊C8—111no—
390C2×C22⋊C8C2×D1111yescharacteristic
391#391—221no—
392#390—221no—
393#386—221no—
394#386—221no—
395#380—111no—
396#380—111no—
397#380—111no—
398#380C2×D1111yescharacteristic
399#340—111no—
400#340—111no—
401#340—111no—
402#340—111no—
403#340—111no—
404#340—111no—
405#340C2×D1111yescharacteristic
406#340C2×D1111yescharacteristic
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11C22×C4⋊C411yescharacteristic
415C22×C11C2×#12011yescharacteristic
416C22×C11C2×#12311yescharacteristic
417C22×C11#57611yescharacteristic
418C22×C11#57711yescharacteristic
419C22×C11#57711yescharacteristic
420C22×C11#57811yescharacteristic
421C2×D11—22no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—22no—
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—41no—
431C2×D11—41no—
432C2×D11—41no—
433C2×D11—41no—
434C2×D11#38514yes—
435C4×C11—22no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11—81no—
439C4×C11—81no—
440C4×C11C2×C4×D411yescharacteristic
441C4×C11C2×C4×D411yescharacteristic
442C4×C11C2×C22⋊Q811yescharacteristic
443C4×C11C2×C22⋊Q811yescharacteristic
444Dic11—22no—
445Dic11—42no—
446Dic11—42no—
447Dic11—81no—
448Dic11—81no—
449Dic11#38514yes—
450C2×#41—114no—
451C2×#41—114no—
452C2×#41—222no—
453C2×#41—222no—
454C2×#41—222no—
455C2×#41—222no—
456C22×Q8—111no—
457C22×D4—111no—
458C22×D4—111no—
459C22×D4—111no—
460C23×C4—21no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—221no—
464C23×C4—221no—
465C23×C4—221no—
466C23×C4C22×D1111yescharacteristic
467C2×M16—114no—
468C2×M16—222no—
469C2×M16—222no—
470C22×C8—111no—
471C22×C8—111no—
472C22×C8—114no—
473C22×C8—222no—
474C22×C8—222no—
475C22×C8C22×D1111yescharacteristic
476C22×C8C22×D1111yescharacteristic
477C4×Q8—228no—
478C4×D4—228no—
479C4×D4—228no—
480C4×D4—228no—
481#117—114no—
482#117—222no—
483#117—222no—
484#117—222no—
485#117—222no—
486#117—222no—
487#117—222no—
488#117—222no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—114no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—222no—
498C2×C4⋊C4—222no—
499C2×C4⋊C4—222no—
500C2×C4⋊C4—222no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—222no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4C22×D1111yescharacteristic
506C2×C4⋊C4C22×D1111yescharacteristic
507C2×C4⋊C4C22×D1111yescharacteristic
508C2×C4⋊C4C22×D1111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C42—221no—
518C2×C42—221no—
519C2×C42—221no—
520C2×C42—221no—
521#107—22no—
522#107—22no—
523#107—222no—
524#107—222no—
525#106—222no—
526#106—222no—
527#106—222no—
528#106—222no—
529C22⋊C8—114no—
530C22⋊C8—114no—
531C22⋊C8—114no—
532C22⋊C8C4×D1114yescomplemented
533#95—21no—
534#95—221no—
535#95—221no—
536#95—221no—
537C2×C11—42no—
538C2×C11C2×#38511yescharacteristic
539C2×C11#291211yescharacteristic
540C2×C11#291311yescharacteristic
541C2×C11#301211yescharacteristic
542C2×C11#301311yescharacteristic
543C2×C11#309611yescharacteristic
544C2×C11#309711yescharacteristic
545D11—24no—
546D11—42no—
547C24—111no—
548C24—111no—
549C24D4×D1111yescharacteristic
550#41—228no—
551#41—228no—
552#41—228no—
553#41—228no—
554C2×Q8—114no—
555C2×Q8—222no—
556C2×Q8—222no—
557C2×D4—114no—
558C2×D4—114no—
559C2×D4—114no—
560C2×D4—222no—
561C2×D4—222no—
562C2×D4—222no—
563C2×D4—222no—
564C2×D4—222no—
565C2×D4—222no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—81no—
576C22×C4—81no—
577C22×C4—111no—
578C22×C4—112no—
579C22×C4—112no—
580C22×C4—112no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—111no—
585C22×C4—112no—
586C22×C4—112no—
587C22×C4—224no—
588C22×C4—224no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—442no—
598C22×C4—881no—
599C22×C4—881no—
600C22×C4—881no—
601C22×C4—881no—
602C22×C4—881no—
603C22×C4—881no—
604C22×C4C2×C4×D1112yes—
605C22×C4D4×D1111yescharacteristic
606C22×C4Q8×D1112yes—
607C22×C4C23×D1111yescharacteristic
608M16—228no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—112no—
614C2×C8—112no—
615C2×C8—228no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8C2×C4×D1112yes—
621C2×C8C2×C4×D1112yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—112no—
630C4⋊C4—112no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—221no—
634C4⋊C4—221no—
635C4⋊C4—221no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—221no—
639C4⋊C4—442no—
640C4⋊C4D4×D1112yes—
641C4⋊C4D4×D1112yes—
642C22⋊C4—81no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—442no—
647C22⋊C4—881no—
648C22⋊C4—881no—
649C22⋊C4—881no—
650C42—224no—
651C42—224no—
652C42—224no—
653C42—442no—
654C11#2084911yescharacteristic, complemented, Sylow
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—112no—
662C23—112no—
663C23—112no—
664C23—112no—
665C23—221no—
666C23—221no—
667C23—221no—
668C23—221no—
669C23—221no—
670C23—221no—
671C23—221no—
672C23—221no—
673C23—221no—
674C23—221no—
675C23C4⋊C4×D1112yes—
676C23C2×D4×D1111yescharacteristic
677Q8—228no—
678D4—228no—
679D4—228no—
680D4—228no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—84no—
700C2×C4—112no—
701C2×C4—112no—
702C2×C4—112no—
703C2×C4—114no—
704C2×C4—114no—
705C2×C4—114no—
706C2×C4—114no—
707C2×C4—112no—
708C2×C4—221no—
709C2×C4—221no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—884no—
727C2×C4—884no—
728C2×C4—884no—
729C2×C4C4⋊C4×D1112yes—
730C2×C4C22×C4×D1111yescharacteristic
731C2×C4C2×D4×D1111yescharacteristic
732C2×C4C2×D4×D1111yescharacteristic
733C2×C4C2×Q8×D1111yescharacteristic
734C2×C4#41×D1111yescharacteristic
735C2×C4#41×D1111yescharacteristic
736C8—22no—
737C8—22no—
738C8—222no—
739C8—222no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—114no—
748C22—222no—
749C22—222no—
750C22—222no—
751C22—222no—
752C22—222no—
753C22—222no—
754C22—222no—
755C22—222no—
756C22—222no—
757C22—441no—
758C22—441no—
759C22—441no—
760C22—441no—
761C22C2×C4⋊C4×D1111yescharacteristic
762C22D11×#12011yescharacteristic
763C22D11×#12311yescharacteristic
764C22#1062328811yescharacteristic
765C22#1062329711yescharacteristic
766C22#1062330611yescharacteristic
767C22#1062330911yescharacteristic
768C4—22no—
769C4—42no—
770C4—42no—
771C4—81no—
772C4—81no—
773C4—114no—
774C4—222no—
775C4—442no—
776C4—442no—
777C4—881no—
778C4—881no—
779C4C4×D4×D1111yescharacteristic
780C4C4×D4×D1111yescharacteristic
781C4D11×C22⋊Q811yescharacteristic
782C4D11×C22⋊Q811yescharacteristic
783C2—42no—
784C2—224no—
785C2—442no—
786C2D11×#38511yescharacteristic
787C2#1307721011yescharacteristic
788C2#1307721211yescharacteristic
789C2#1307791511yescharacteristic
790C2#1307793211yescharacteristic
791C2#1307856711yescharacteristic
792C2#1307858411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1852C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1852D11
hypocenterC11#20849
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10622494C2semidirect
3. C2×#10622493C2semidirect
6. #13068818C2semidirect
7. #13068817C2semidirect
8. #13068813C2semidirect
9. #13068812C2semidirect
10. #13068810C2semidirect
11. #13068809C2semidirect
12. #13068802C2semidirect
13. #13068334C2semidirect
14. D11×#340C2semidirect
15. C11×#1852C2semidirect
53. #10622340C4semidirect
117. C2×#4313C2×C4semidirect
120. C2×C8×D11C2×C4semidirect
137. C11×C22⋊C8C2×C4semidirect
142. C22⋊(C11⋊C8)C2×C4semidirect
143. (C2×D11)⋊C8C2×C4semidirect
144. (C2×D11)⋊C8C2×C4semidirect
271. #1852D11semidirect
532. C22⋊C8C4×D11semidirect
654. C11#20849semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106230352
C2×#106224942
C2×#106224932
C2×#106223402
#130712052
#130688182
#130688172
#130688132
#130688122
#130688102
#130688092
#130688022
#130683342
D11×#3402
C11×#18522
#2084911